https://arxiv.org/api/6p1So1cQ2tPpnJsZ26o79eLEB48 2026-10-01T02:46:54Z 40 2100 0 http://arxiv.org/abs/2609.38688v1 2026-09-30T00:16:20Z

In liquid ammonia, an imbalance between available hydrogen-bond donor and acceptor sites limits water-like tetrahedral connectivity, leaving sparse and short-lived associations within a densely packed liquid. We ask whether quantum-sensitive local rearrangements can nevertheless contribute appreciably to diffusion in this weakly connected liquid. We compare classical and thermostatted ring polymer molecular dynamics from 170 to 250 K using an r$^2$SCAN-trained machine learning force field. Ammonia can change its molecular geometry as the nitrogen atom passes through the plane of the three hydrogen atoms, a motion known as pyramidal inversion. Nuclear quantum effects increase the inversion rate and reduce its apparent activation energy. Inversion events are accompanied by transient reductions in hydrogen-bond coordination and local density within the first solvation shell. Although nuclear quantum effects lower density and viscosity throughout the studied range, diffusion remains only weakly affected in the warmer liquid. The quantum enhancement of diffusion emerges below approximately 210 K and reaches 18% at 170 K, tracking the enhancement of cage escape. These observations support an inversion-assisted contribution to diffusion, in which a spatially localized, quantum-sensitive internal motion couples to cage relaxation without a persistent tetrahedral network.

2026-09-30T00:16:20Z 37 pages, 13 figures Minwoo Kim Hido Woo Taeyong Park Ji Woong Yu Won Bo Lee http://arxiv.org/abs/2609.38493v1 2026-09-29T20:21:30Z

We provide one full solution, and another nearly complete solution, to two problems from Jim Propp's 1999 article "Enumeration of matchings; problems and progress" (namely, Problems 30 and 31) involving divisibility properties of the number of matchings of two non-bipartite triangular graphs. We extend our method of proof of the second problem to show that the number of matchings of any graph composed of tetrahedral cells, such that the number of cells is suitably few relative to the number of vertices, is divisible by a power of 3; in particular, we then exhibit a collection of non-planar graphs whose number of matchings is divisible by 3.

2026-09-29T20:21:30Z 15 pages, 20 figures Aidan Dunkelberg http://arxiv.org/abs/2609.38351v1 2026-09-29T18:12:11Z

Three-dimensional flood propagation through the Bhote Koshi--Langtang Khola junction at Syabrubesi, Nepal, is studied using an incompressible free-surface model. The calculation is motivated by the August 2026 flood and examines the passage of an imposed inflow through the local bends and changes in channel width. The Navier--Stokes equations and an interface transport equation are solved on unstructured tetrahedral meshes constructed from pre-event terrain data. For an inlet speed of $10\,\mathrm{m\,s^{-1}}$, the solution indicates surface speeds above $40\,\mathrm{m\,s^{-1}}$. The advancing front spreads across the junction; as the flow develops, water deepens and slows around the bend. Higher speeds persist in the confined upstream and downstream regions.

2026-09-29T18:12:11Z Rainald Löhner Harbir Antil http://arxiv.org/abs/2609.36277v1 2026-09-28T21:06:52Z

Existing protein geometry models typically represent molecular surfaces using local geometric features such as sampled points, normals, and curvature. While effective for capturing exposed molecular shape, these representations do not explicitly model the volumetric organization beneath the surface or provide a consistent coordinate system for residue-wise volumetric structure. We introduce Protein-TetSphere, a registered residue-wise volumetric representation for proteins. Each protein chain is tetrahedralized to obtain local volumetric regions associated with individual residues, which are then registered to a shared fixed-topology tetrahedral reference and represented in a common Laplacian basis. This registration establishes consistent volumetric coordinates across residues, enabling local three-dimensional deformation to be integrated with surface and chemical information in a multimodal protein representation. We evaluate Protein-TetSphere on ligand-binding pocket classification, protein--protein interface prediction, and de novo protein binder design. Across the three tasks, Protein-TetSphere improves ligand-binding pocket balanced accuracy from $0.795$ to $0.826$, Pinder-Pair/Site AUROC from $0.914/0.852$ to $0.932/0.866$, and binder-design success from $14.95\%$ to $19.90\%$ on the BoltzGen Challenge Set and from $27.62\%$ to $32.19\%$ at the ProtDBench backbone level. These results show that registered volumetric geometry provides complementary spatial information beyond molecular surfaces across protein recognition, interaction, and design.

2026-09-28T21:06:52Z Siyuan Chen Cai Zhou Jinrui Zhang Zhaokang Liang Taku Komura Wojciech Matusik Stephen Bates Tommi Jaakkola Wengong Jin Peter Yichen Chen Minghao Guo http://arxiv.org/abs/2609.33478v1 2026-09-27T11:44:54Z

A reproducible method for sustained catalyst-mediated growth of diamond and cubic boron nitride (cBN) wires has yet to be established. Catalyst-assisted growth has produced carbon and boron nitride nanotubes and a wide range of elemental, compound and alloy nanowires. Diamond and cBN wires could combine high specific stiffness and strength with heat conduction and electrical insulation. I propose vapor-liquid-solid (VLS) and vapor-solid-solid (VSS) routes in which temperature, feed, catalyst or starting contact changes between formation of the first diamond or cBN segment and its continued growth. The approaches include switching from carbide or boron-rich starter wires, depositing catalyst on selected facets of existing crystals, and using local solid feedstock to supply the catalyst during initial growth. Historical diamond-whisker reports motivate renewed tests of diamond-metal contacts. The proposed experiments ask whether these contacts can favor tetrahedral bonding while maintaining a supply of atoms to the growing wire. Both single-crystal and polycrystalline products, from nanometer to micrometer and larger diameters, are of interest.

2026-09-27T11:44:54Z Perspective; 64 pages, including 30 pages of Supporting Information; 8 figures Rodney S. Ruoff http://arxiv.org/abs/2609.31443v1 2026-09-25T16:02:00Z

Low-order refined (LOR) preconditioning replaces a high-order operator with a low-order discretisation on a refined nodal mesh. For tensor-product elements, the two operators are spectrally equivalent with bounds independent of the polynomial order $P$, but the construction does not extend directly to simplex and mixed-element discretisations. This work makes two contributions: it extends LOR preconditioning to simplex and mixed-element discretisations, including triangular, tetrahedral, and prismatic elements, and establishes a generalised Vandermonde transformation linking the modal and nodal LOR formulations, showing that the resulting preconditioned spectra and Krylov convergence are independent of the high-order basis. Numerical experiments show controlled iteration growth on triangular meshes despite increasing condition number, and controlled iteration counts up to $P=6$ on tetrahedral, prismatic, and mixed-element meshes. A single algebraic multigrid V-cycle per outer iteration gives the best balance of iteration count and cost. The method is applied to a production incompressible Navier-Stokes simulation of a race-car front-wing and wheel configuration, discretised on a mesh of $2.87\times10^6$ mixed prismatic and tetrahedral elements giving $32.2\times10^6$ pressure degrees of freedom at $P=3$. LOR reduces the mean pressure conjugate gradient (CG) iteration count from $235.3$ to $5.5$, and the pressure-solve time over 1000 timesteps by 16.1%, relative to the default production static-condensation diagonal preconditioner in Nektar++. The one-time cost of constructing the LOR preconditioner is amortised over the production simulation.

2026-09-25T16:02:00Z Parv Khurana Henrik Wüstenberg Spencer J. Sherwin David Moxey Julien Hoessler Athanasios Chatzopoulos http://arxiv.org/abs/2609.31277v1 2026-09-25T13:49:52Z

P-type transparent conducting materials (TCMs) remain scarce, limiting progress in transparent electronics and tandem photovoltaics. Here, we perform a high-throughput computational search across CuI-based ternary X--Cu--I compounds using the minima hopping method combined with density functional theory. Filtering for thermodynamic stability, optical transparency, and light hole effective mass, we identify 58 candidate p-type TCMs, of which 49 are previously unreported. Twenty are p-type degenerate semiconductors with intrinsic hole carriers, including Cu$_2$FI$_2$ (calculated gap 3.75 eV, hole effective mass $0.262\,m_0$). We further use this dataset to revisit the chemical modulation of the valence band (CMVB) design rules, originally formulated for Cu-based delafossite oxides. Four generalizations emerge: linear Cu coordination is not required, as tetrahedral coordination (CN = 4) is compatible with p-type TCM character; the mechanism extends to halide-based systems with I $5p$ anion states; the Cu $d$ state energy center $ε_d$ is a quantitative descriptor for valence band dispersion; and Cu undercoordination in monovalent-anion hosts drives intrinsic p-type carrier generation through stoichiometric charge balance. These results establish a generalized computational framework for the design of p-type halide TCMs.

2026-09-25T13:49:52Z Michael Seifert Miguel A. L. Marques Silvana Botti http://arxiv.org/abs/2609.30162v1 2026-09-24T17:18:38Z

We study the spin-1/2 nearest-neighbor Heisenberg model on the breathing pyrochlore lattice in the mixed ferro-antiferromagnetic regime, where one tetrahedral sublattice is antiferromagnetic and the other ferromagnetic. The classical ground-state manifold is then that of the nearest-neighbor face-centered-cubic (fcc) antiferromagnet built from composite tetrahedral moments. Classical Monte Carlo simulations and the self-consistent Gaussian approximation show that thermal order-by-disorder lifts its subextensive degeneracy and selects the collinear Type-I state with wave vector $X=(1,0,0)$ through a strongly first-order transition. Pseudofermion functional renormalization group calculations for $S=1/2$ and $S=1$ reveal a nonmagnetic window adjacent to the decoupled antiferromagnetic-tetrahedron limit, beyond which $X$ order reappears. Density matrix renormalization group calculations show that this window is not featureless: the antiferromagnetic tetrahedra develop nearly ideal tetramer correlations, with four bonds carrying $\langle\mathbf{S}_i\cdot\mathbf{S}_j\rangle\simeq-1/2$ and the two opposite bonds $\simeq+1/4$, while the structure factor retains broad maxima at $X$. A third-order effective Hamiltonian in the tetrahedral-singlet manifold explains this: reversing the sign of the inter-tetrahedron coupling converts Tsunetsugu's dimer selection into a uniform tetramer selection, as confirmed by exact diagonalization. A dynamic high-temperature expansion traces how local tetrahedral excitations give way to low-energy $X$-centered spectral weight. Finally, we place density-functional parameters for eight structures of spin-3/2 breathing chromium thiospinels in the classical phase diagram. The mapping reproduces the $\mathbf{k}=(1,0,0)$ order of CuInCr$_4$S$_8$, accounts for the absence of order in LiGaCr$_4$S$_8$, and predicts Type-I order for LiInCr$_4$S$_8$.

2026-09-24T17:18:38Z 38 pages, 23 figures, 6 tables Sourin Chatterjee Kelvin Salou-Smith Benedikt Schneider Imre Hagymási Arnaud Ralko Johannes Reuther Jeffrey G. Rau Karlo Penc Harald O. Jeschke Ludovic D. C. Jaubert Yasir Iqbal http://arxiv.org/abs/2609.30008v1 2026-09-24T15:48:53Z

This paper develops a divergence-free, inf-sup stable, optimally convergent and pressure-robust finite element method for the three-dimensional Stokes problem on curved domains. The geometry is approximated by an isoparametric tetrahedral mesh, while the velocity space is obtained from Scott--Vogelius spaces on an Alfeld split by the Piola transform. The discrete inf-sup condition is proved using suitable face bubble functions. The insufficient accuracy of quadrature rules on curved triangular interfaces leads to a consistency error that may cause suboptimal convergence. The remedy is to introduce a suitable consistency correction without stabilization terms. Moreover, commuting operators on curved domains are constructed from local commuting interpolants and shown to be globally conforming. The operators are used to approximate the load and obtain a pressure-robust discretization. Numerical examples are provided to validate the theoretical results.

2026-09-24T15:48:53Z Wei Chen Zhen Liu http://arxiv.org/abs/2609.29810v1 2026-09-24T13:46:31Z

Piezoelectricity is a key phenomenon in solid-state physics and has significant technological relevance. In teaching, however, it is often treated either without a historical context or an explicit link to the microscopic crystal structure, meaning that a crucial level of understanding remains untapped. This study combines the history of the discovery of piezoelectricity with its physical description within a didactically coherent framework. Building on the work of the brothers, Jacques and Pierre Curie (1880 - 1882), it demonstrated how investigations into pyroelectricity led to the identification of polarization induced by mechanical compression in hemihedral crystals such as tourmaline and quartz. The development from early qualitative experiments towards the first quantitative determination of piezoelectric constants is traced in a structured manner. Using low quartz as an example, the microscopic cause of piezoelectricity was attributed to the asymmetric displacements of silicon and oxygen ions within the orthosilicate ion tetrahedral network. This leads to the formation of macroscopic polarization owing to uncompensated dipole moments in the crystal lattice. The direct and reciprocal piezoelectric effects are qualitatively distinguished and discussed in the context of mechanical-electrical coupling. The article is aimed at students in physics and engineering as well as lecturers. It was conceived as a didactic review article (tutorial article) and serves as a structured introduction to the physical and historical foundations of piezoelectricity.

2026-09-24T13:46:31Z 13 pages, 11 figures, essential info Ruediger G. Ballas Nataliya Koev http://arxiv.org/abs/2609.29153v1 2026-09-24T07:30:19Z

For every integer $n \ge 2$, we construct explicit tetrahedral counterexamples showing that repeated longest-edge (LE) n-section refinement does not, in general, preserve shape regularity, contrary to long-standing conjectural expectations. For $n = 2$, the construction disproves the finite-family conjecture put forward by Adler in 1983 and the non-degeneracy conjecture for tetrahedral longest-edge bisection formulated by Rivara and Levin in 1992. It also shows that the sharper higher-dimensional diameter decay suggested by Stynes in 1983,following his 1980 planar finite-similarity result, cannot hold for arbitrary tetrahedra. For $n = 3$, it disproves the published non-degeneracy conjecture for tetrahedral longest-edge trisection formulated in 2011 by Suárez, Abellón, Abad and Plaza on the basis of numerical experiments. The resulting infinite descendant sequences violate both the minimum and maximum angle conditions. For $n \ge 3$, the selected edge is always the unique longest edge at every refinement step. The two-step recurrence used in the construction exhibits two distinct degeneration behaviors: a flat-tetrahedron regime for $2 \le n \le 5$ and a skinny-tetrahedron regime for $n \ge 6$. The degenerating sequences can also be realized within conforming partitions generated by the conforming LE n-section algorithm. For both the classical and the conforming LE n-section algorithms, the maximal element diameter tends to zero as the number of refinement steps tends to infinity, regardless of which longest edge is chosen. Thus diameter convergence, and even conformity, do not prevent shape degeneration. These algorithms should therefore be used with care in applications requiring uniform shape regularity.

2026-09-24T07:30:19Z Sergey Korotov http://arxiv.org/abs/2609.31761v1 2026-09-23T20:28:46Z

Mechanical metamaterials are materials that, by virtue of their microstructural architectures, exhibit mechanical properties not often found in nature: for example, auxetic mechanical metamaterials are materials that possess a negative Poisson's ratio in response to deforming forces. However, outside of relatively simple crystalline, lattice-based, or repeating-pattern architectures composed of mostly identical unit cells, mechanical metamaterials like auxetics are notoriously difficult to design, particularly across all three dimensions. Here we show that, for any structure that can be decomposed into triangular or tetrahedral meshes, those structures can be subjected to a simple transformation that that creates conditions within those triangular or tetrahedral simplexes that, regardless of their individual geometries, introduces a counter-rotating polygon/polyhedron mechanism that both guarantees a negative Poisson ratio and allows locally programmable mechanical properties. We apply this "shrink-and-wrap" construction to generate mechanical metamaterials from increasingly complex 3D structures, first from simple (convex) polyhedrons; then, to designs with arbitrarily large numbers of vertices and designed using constructive solid geometry (CSG) and 3D scanning; and, ultimately to 3D objects generated from videos captured by mobile phone camera -- making potentially any object or geometric structure designed or found in the real world transformable into a mechanical metamaterial. We show that these monolithic auxetic constructions remain readily 3D-printable via additive manufacturing techniques. We expect this piecewise approach to designing arbitrarily complex mechanical metamaterial structures can enable numerous potential applications where programmable internal reconfigurations and/or force redirection are required across and throughout their 3D geometries.

2026-09-23T20:28:46Z 20 pages, 4 main figures, 4 supplementary figures. Fnu Braminder, Issac Varghese, and Noah Kim contributed equally to this manuscript Fnu Braminder Mechanical Metamaterials and Kinetic Devices Issac Varghese Mechanical Metamaterials and Kinetic Devices Noah Kim Mechanical Metamaterials and Kinetic Devices Alyssa Thomas DeCruz Department of Biomedical Engineering, College of Engineering and Applied Sciences Eric A. Josephs Mechanical Metamaterials and Kinetic Devices Department of Biomedical Engineering, College of Engineering and Applied Sciences http://arxiv.org/abs/2609.28301v1 2026-09-23T15:46:47Z

The objective of this paper is to identify a finite group based on the orbit of a vector under its action. When a finite group acts unitarily on a Hilbert space, the associated Gram matrix lies in the group algebra and satisfies identities that encode the algebraic group structure. We ask about the converse: Given a Gram matrix obtained from the orbit of a vector under the group action, can one recover the underlying \emph{abstract} group structure? Our main result identifies a short list of conditions on a family of orthogonal matrices that force the family to be the right regular representation of a finite group. Building on this characterization, we develop a staged optimization framework that enforces these conditions progressively. Numerical experiments on the dihedral group $D_4$ and the tetrahedral rotation group $A_4$ recover $D_4$ exactly and all twelve $A_4$ matrices up to modest precision.

2026-09-23T15:46:47Z 23 pages, AMS LaTeX Bernhard G. Bodmann Reshma Sabnam http://arxiv.org/abs/2609.22955v1 2026-09-19T11:11:42Z

We extend the high-order Zipped Finite Element Method to three-dimensional polyhedral elements. The construction relies on a local sub-tetrahedralization obtained by triangulating the polygonal faces and connecting the resulting vertices to a suitable interior point. High-order shape functions are constructed as linear combinations of standard finite element basis functions, with coefficients chosen to ensure exact polynomial reproduction on the faces and in the element interior while preserving global C0-conformity. We further introduce a QR-based strategy as a systematic alternative to the heuristic procedure that was adopted for the two-dimensional case. The QR-strategy is more systematic and robust than the heuristic strategy, while being independent of the spatial dimension and avoiding geometric alignment tests and problem-dependent tolerances. The resulting method is formulated for a diffusion-reaction problem and numerically assessed through three-dimensional convergence tests, confirming the expected optimal polynomial order of accuracy.

2026-09-19T11:11:42Z Stefano Berrone Gioana Teora http://arxiv.org/abs/2609.20618v1 2026-09-17T16:02:57Z

Minimizing magnetic damping while understanding spin-lattice interactions remains a key challenge for magnonics. We show site-specific Al/Li ordering in spinel ferrites drives a ferrimagnetic insulating state, quenching the Fermi-level density of states. \textit{Ab initio} calculations reveal collective acoustic modes alongside sub-lattice-selective optical modes on tetrahedral and octahedral networks, providing a microscopic understanding of substitution-driven spin dynamics. Crucially, the low-frequency magnon and acoustic phonon modes intersect, driving strong hybridization for low-loss technologies.

2026-09-17T16:02:57Z 8 pages and 3 figures Hari Paudyal Yuri Suzuki Michael E. Flatté Durga Paudyal http://arxiv.org/abs/2609.18788v1 2026-09-16T15:09:06Z

We present a fixed nondegenerate tetrahedron with a nested largest-dihedral-anglebisection branch that collapses onto a unit edge. The selected dihedral angles to bisect are uniquely largest ones at every bisection step. Some face angles of the branch elements tend to zero, the corresponding diameter-to-inradius ratio diverges, and the diameters of the elements produced do not tend to zero, although every dihedral angle stays uniformly away from both 0 and π and all face and dihedral angles satisfy a uniform maximum-angle bound. The proof is based on an exact invariant-range argument. This example shows that the largest-dihedral-angle bisection algorithm can produce degenerating tetrahedral partitions.

2026-09-16T15:09:06Z Sergey Korotov Jérôme Michaud http://arxiv.org/abs/2609.18721v1 2026-09-16T14:22:18Z

In a frustrated spin system, highly entangled eigenstates can form a separable thermal mixture. We study this distinction for four spin-$1/2$ moments on a tetrahedron, the elementary unit of the pyrochlore lattice, with the general four-parameter exchange Hamiltonian. Tetrahedral symmetry allows a restricted search over thermal-state decompositions to be carried out by linear optimization, yielding an upper bound on multipartite concurrence and explicit separable decompositions where this bound vanishes. At low temperature, the concurrence maps show extended separable regions near the all-in--all-out limit, whereas suppression near the spin-ice point is narrowly localized. Heating broadens the latter region as nearby multiplets are repopulated. The optimization identifies fully separable thermal states even when the eigenstate-averaged concurrence remains large. Negativity independently confirms finite-temperature entanglement in selected coupling regions. A mixed-state stabilizer Rényi diagnostic, used to explore quantum magic, favours different couplings and can increase locally with temperature. These results connect thermal entanglement to the splitting and population of symmetry multiplets, and provide a practical basis for identifying frustrated spin configurations for studies of quantum resources beyond the ground-state limit.

2026-09-16T14:22:18Z 11 Pages, 13 Figures, Original Research Article Reza Pourkhodabakhshi Francis Dominie Deep Gajera Stephanie H. Curnoe http://arxiv.org/abs/2609.18040v1 2026-09-16T02:40:26Z

Sound event localization and detection (SELD) systems often rely on first-order Ambisonics (FOA) input, whereas obtaining useful FOA representations from irregular microphone arrays remains challenging. This paper proposes a two-stage SELD framework that learns a task-oriented, FOA-compatible representation from microphone-array signals. A neural residual encoder first refines conventional FOA encoding through a signal-dependent correction. A teacher--student scheme then transfers event and spatial knowledge from theoretical FOA representations through frame-level permutation-invariant knowledge distillation. Experiments on synthetic scenes with tetrahedral and 12-channel Benchmark arrays, together with real stationary-source recordings from the LOCATA dataset, show that teacher guidance consistently improves downstream SELD performance and substantially reduces localization error. Signal-level analysis further shows that lower FOA reconstruction error does not necessarily correspond to better SELD performance, indicating that the distilled representation is optimized primarily for task-relevant spatial information rather than strict FOA reconstruction.

2026-09-16T02:40:26Z Submitted to ICASSP 2027 Jiachen Liu Yin Cao Ming Wu Jun Yang http://arxiv.org/abs/2609.17216v1 2026-09-15T14:02:23Z

Simulated electromyograms are used to understand what an electrode records, to test decomposition and estimation algorithms on signals with known ground truth, and to train learning-based decoders. Most simulators fix the geometry to a cylinder or a slab, or stop at the lead field and leave the rest to the user. We present emgforge, an open pipeline that takes a labelled MRI segmentation of a limb to surface EMG in one command: a tetrahedral mesh with conductivity tensors aligned with each muscle's fibres; one reciprocal finite-element solve per electrode, valid for every fibre of every muscle; fibre beds that are straight or follow the muscle's shape; a motor-unit pool obeying the size principle; motor-unit action potentials on any electrode layout; and a motoneuron-pool and twitch layer that turns a drive or a movement into interference EMG and force. We describe the pipeline stage by stage, and at each stage we show, with an example, why the choice was made. The step that turns a lead field into a single-fibre action potential -- direct line-source synthesis -- is checked against a closed-form solution ($r = 1.0000$, zero lag), and the whole chain against fifty checks with numeric criteria from the physiological literature. We then use the pipeline for four studies: what an electrode sees as a function of depth, fat, spacing and montage; whether fibre geometry changes the signal; how much crosstalk a grid over one muscle receives from its neighbours; and how interference EMG scales with drive. The code, the validation suite and three datasets with ground truth are released.

2026-09-15T14:02:23Z 30 pages, 12 figures, 6 tables. Code, validation suite and datasets: https://github.com/dhalatsis/emgforge (tag arxiv-v1) Dimitrios Halatsis Noura Ezaz-Nikpay Pranav Mamidanna Dario Farina http://arxiv.org/abs/2609.16686v1 2026-09-15T06:07:15Z

Estimating deformable object states remains a fundamental challenge in robotics and simulation. We propose a novel factor graph-based framework for probabilistic mesh state estimation of deformable objects. The method directly updates a tetrahedral mesh, a rich and physically-grounded representation of an environment, by combining physics priors, noisy sensor measurements, and temporal smoothness constraints within a unified probabilistic formulation. The estimation problem is posed as a nonlinear least-squares optimization and solved using Levenberg-Marquardt. Ex vivo central-airway obstruction experiments and simulations on deforming cube models demonstrate reliable and accurate reconstruction under both rigid motion and deformation, highlighting the potential of this probabilistic approach for principled, measurement-driven mesh state estimation in deformable object reconstruction.

2026-09-15T06:07:15Z 8 pages Lidia Al-Zogbi Fangjie Li Samuel Tobin James Ferguson Nithesh Kumar Alejandro Chara Kuan-I Chung Mingxing Rao Ayberk Acar Susheela Sharma Stern Robert Webster Daniel Moyer Alan Kuntz Caleb Rucker Tucker Hermans Jie Ying Wu http://arxiv.org/abs/2609.14797v1 2026-09-13T21:18:25Z

We prove that every configuration of four through eight points in three-dimensional space, with no four points coplanar, has a connected full geometric flip graph under $2 \leftrightarrow 3$ flips. Every point remains fixed and present throughout the sequence. The proof brings each tetrahedralization into placing form at a convex hull vertex: the tetrahedra not incident to that vertex fill the convex hull of the remaining points. This reduction allows us to establish connectivity by induction, using the connectivity of regular tetrahedralizations. The main geometric tool is radial projection, which turns the tetrahedra incident to a hull vertex into a planar triangulation. When this planar triangulation is regular, varying its lifting heights produces legal spatial flips that progressively shrink the region occupied by the incident tetrahedra and reach placing form. Planar lifting criteria and compatibility constraints between the projections at different hull vertices resolve the remaining small cases. For eight points, at most 35 flips are needed to reach placing form.

2026-09-13T21:18:25Z Marc Khoury http://arxiv.org/abs/2609.13449v1 2026-09-11T19:08:16Z

We develop a discrete design theory for cofactor reference forms that preserve the complete finite-element elasticity tangent. A fixed continuous potential generates the coefficient, while the variation space and quadrature determine compatibility. We classify the exact local potential spaces for all-order tensor elements, anisotropic spaces, cubic serendipity and quadratic tetrahedra. At a stress-free Mooney-Rivlin state with a common positive material-coefficient sum, a convex loss expresses the attainable quadrature-point material margin. The optimum is attained; under stated space and sampling assumptions, its ideal value is attained precisely when the physical identity potential is compatible. A conforming fixed-candidate example proves a strict margin loss, linear in curvature amplitude and uniform in cell size, under displacement enrichment. Explicit positive candidates accompany this restriction. A Gram identity gives the sharp constant-coefficient defect at a prescribed margin in the stated norm. Compatible and reference-defect-corrected forms retain the original tangent through a deformation-independent external-boundary Hessian; equal potential traces give equal exact assembled gauges. Quadratic tensor geometry admits a stress-free physical coercivity bound uniform in mesh size and displacement order under explicit material, shape, quadrature and boundary assumptions. Certified curved tetrahedral shear families with zero recovered cell pressure establish finite-deformation regimes, while a loaded pressure-curvature counterexample identifies their limitation. The theory and observations distinguish local exactness, material certificates, complete-reference coercivity and unchanged equations.

2026-09-11T19:08:16Z 57 pages, 4 figures Yanlin Liu The University of Melbourne Kaixiang Yao Southern University of Science and Technology Chao Huang Shanghai Jiao Tong University Yao Shen Shanghai Jiao Tong University http://arxiv.org/abs/2609.13371v1 2026-09-11T18:00:00Z

We introduce a general mechanism for engineering moment-selective temporal designs with hierarchically structured aperiodic drives. At special control settings where the driven dynamics is constrained by a finite symmetry group, lower-order moments can already reproduce Haar statistics while a selected higher-order deviation remains nonzero. A small static detuning from such a setting generically produces an exponentially long lifetime whose exponent scales inversely with the square of the detuning. We illustrate this mechanism in qubit systems through exact Fibonacci and silver-mean constructions with tetrahedral and icosahedral resonances, for which the first retained non-Haar moments occur at orders $3$ and $6$, respectively. We further show that stochastic control fluctuations produce a qualitatively different cutoff from coherent detuning. Finally, we propose a finite-time signature of the long-lived moment that can be measured without requiring observations over exponentially long times.

2026-09-11T18:00:00Z 5 pages + supplemental material Yang Peng http://arxiv.org/abs/2609.10503v1 2026-09-09T17:37:54Z

Geodesic polar coordinates (GPCs) provide an intrinsic parameterization over curved surfaces, but their accurate estimation remains challenging, particularly in the presence of anisotropic metrics, high curvature and complex topology. We introduce iLogMap, a method for computing GPCs in curved domains that recasts the angular component of the logarithmic map to a ground-state magnetic eigenproblem over the circumferential direction field of geodesic distance. Our method effortlessly extends to anisotropic metric tensors and solid volumes, enabling cylindrical and spherical parameterizations in tetrahedral meshes. Experiments on diverse shapes with varying genus confirm competitive angular accuracy and reduced metric distortion relative to heat-based methods, with improved performance on surfaces with boundary and domains with anisotropy. We demonstrate the utility of iLogMap in computational cardiology applications, where we use it to initialize spiral phases on atrial surfaces and estimate local activation patterns in ventricular models.

2026-09-09T17:37:54Z Tomás Banduc Simone Pezzuto Francisco Sahli Costabal http://arxiv.org/abs/2609.10242v1 2026-09-09T14:32:59Z

We study the spatial $(n+1)$-body problem formed by one heavy central mass together with $n$ equal masses placed on a single orbit of a polyhedral rotation group $H\in\{T,O,I\}$, so that $n=|H|\in\{12,24,60\}$. Imposing the symmetry $q_{L}=L\,q_{I}$ for $L\in H$ reduces the problem to a single $2π$-periodic reference curve, with reduced action $A_{H}=A_{0}+\varepsilon A_{1}$, in which $\varepsilon$ is the inverse central mass and $A_{0}$ is the Kepler action. At $\varepsilon=0$ the critical set contains, as one connected component, the five-dimensional manifold of Kepler ellipses of minimal period $2π$, which we prove to be a nondegenerate critical manifold. A Lyapunov--Schmidt reduction along this manifold turns the continuation problem into the search for nondegenerate critical points of an explicit function $Φ(e,ψ)$ of the eccentricity $e$ and the spatial orientation $ψ$, a nondegeneracy we verify by a computer-assisted proof. We thereby obtain, for each of the three groups, families of periodic solutions of the $(n+1)$-body problem with $n+1\in\{13,25,61\}$ bodies, bifurcating from Kepler ellipses and carrying the full tetrahedral, octahedral, or icosahedral symmetry.

2026-09-09T14:32:59Z 30 pages, 2 figures Kevin Constantineau Carlos García-Azpeitia Jean-Philippe Lessard http://arxiv.org/abs/2609.09617v1 2026-09-09T02:22:13Z

A symmetric representation of Minkowski spacetime is constructed by combining a normalized fourth-order Hadamard transformation with an imaginary temporal coordinate. The resulting complex coordinates $q^a$ distribute time and space equally among four components and transform the Minkowski metric into a Euclidean-form complex bilinear metric. The four Hadamard spatial sign vectors form a regular tetrahedron and appear simultaneously in the transformed Dirac and Maxwell operators. The Dirac matrices satisfy a Euclidean-form Clifford algebra and contain tetrahedral combinations of Pauli matrices, whereas the Riemann--Silberstein Maxwell matrices realize the corresponding spin-1 structure. A gauge-invariant QED Lagrangian is formulated in the same coordinates. In Fourier space, the Dirac and Maxwell systems are governed by the common invariant $κ_aκ^a$, while the complete Maxwell operator admits an exact rectangular Clifford-like factorization. The formulation is further extended to the weak-field Einstein--Dirac--Maxwell system. In harmonic gauge, the linearized gravitational field is governed by the same scalar wave operator $\Box_q$, while gravitational corrections to the Dirac and Maxwell equations enter through the perturbed tetrad, spin connection, and curvature. This common principal-operator structure suggests shared spectral kernels and scalar-wave preconditioning for coupled field solvers.

2026-09-09T02:22:13Z Farhad Aghili http://arxiv.org/abs/2609.09446v1 2026-09-08T20:53:22Z

Lutetium hydrides (LuH$_x$, $1.75 \leq x \leq 3$) form a diverse series of phases, several of which superconduct under pressure. Characterizing their electronic properties has remained challenging owing to a high propensity for hydrogen defect formation, and recent angle-resolved photoemission (ARPES) measurements reveal puzzling flat-band regions that position these materials as candidates where superconductivity and flat-band physics may intersect. Here, by combining density functional theory, dynamical mean-field theory, and the constrained random-phase approximation, we uncover the microscopic origin and correlation nature of these flat bands. Across all compositions, the screened on-site Coulomb interaction is larger for H-s states than for Lu-$d$ states due to compact hydrogen orbitals. Nevertheless, these systems remain weakly correlated metals: the nearly filled H-$s$ shell admits little charge fluctuation, so its large interaction acts as a static level shift rather than a source of correlation. Although hydrogen primarily occupies tetrahedral sites at $x=2$, we discover that anti-site defects--where hydrogens occupy slightly unfavorable octahedral sites--generate both the ARPES flat-band features and the low-energy optical absorption peak, attesting to the usual defective nature of such materials in experimental samples. We further find that correlation strength is governed primarily by hydrogen orbital filling at these sites rather than the interaction magnitude itself. Consequently, we identify hydrogen orbital filling as the fundamental organizing principle dictating correlation and low-energy flat-band physics in lutetium hydrides.

2026-09-08T20:53:22Z 12 pages, 6 figures Anmol Lamichhane Adam Denchfield Hyeondeok Shin Panchapakesan Ganesh Russell J. Hemley Hyowon Park http://arxiv.org/abs/2609.07760v1 2026-09-07T17:06:40Z

The Hemoglycin polymer of glycine derived from space is terminated by iron and silicon to form a three-dimensional regular lattice with a high density of silicon tetrahedral vertices. Divalent cation bridges bypass vertices to facilitate electron conduction axially from layer to layer of the lattice. In principle, the exact distribution of Mg or Ca ions around each vertex can encode a very large amount of information. In space where the polymer forms in a molecular cloud the current derived from photon input will fade but in-fall hemoglycin in life forms on habitable planets like Earth, could be contained behind lipid electronic barriers of the nervous system in neurons or glia. Energy minimization of the permutations for magnesium or calcium occupancy showed deeper binding for calcium-dominated configurations. A low energy state with two independent magnesium to calcium substitutions appears to be key to the maintenance of long-term chemical modification. This state could be read via a pulse train that induced the matching spatial distribution of calcium to render adjacent insulating lattice regions conductive and provide a completed conduction path, signaling recognition. Writing of information may involve spatial modulation of the Na/Ca exchanger within the lipid membrane.

2026-09-07T17:06:40Z 17 pages,9 Figures, 1 Table Julie E. M. McGeoch Malcolm W. McGeoch http://arxiv.org/abs/2609.06723v1 2026-09-06T16:55:21Z

Meshes remain the most practical representation for geometry reasoning and integration into graphics pipelines, yet existing reconstruction methods struggle to produce high-quality meshes. Most state-of-the-art approaches initially learn an intermediate representation (NeRF/3DGS) and treat mesh extraction as a post-processing step, which often leads to oversmoothed surfaces or poor quality meshes with excessive triangle counts.Existing mesh-native optimization methods alleviate some of these issues but suffer from fixed-resolution discretizations and unstable optimization behavior. In this paper, we introduce an adaptive mesh-based optimization framework and a practical mesh rendering technique to address these challenges. Our representation combines an optimizable Delaunay-triangulated tetrahedral grid with a multi-resolution hash grid. The former is refined through point pruning and insertion, while the latter provides latent features for SDF/appearance value predictions. We use volumetric rendering to bootstrap a coarse geometry while leveraging mesh-based rendering for recovering fine-grained details. Additionally, we propose a differentiable, rasterization-based depth-offset rendering formulation, reducing geometric artifacts and improving reconstruction quality. Our method significantly outperforms existing mesh optimization approaches across a variety of object-centric benchmarks while being competitive with state-of-the-art NeRF/3DGS methods.

2026-09-06T16:55:21Z Accepted to SIGGRAPH Asia 2026 Conference Papers | Project page: https://johannes-weidenfeller.github.io/adele | Code: https://github.com/johannes-weidenfeller/adele Johannes Weidenfeller Shaofei Wang Philipp Fürnstahl Siyu Tang 10.1145/3829340.3842214 http://arxiv.org/abs/2609.06613v1 2026-09-06T13:59:43Z

The translational dynamics usually decouples earlier than the rotational in supercooled liquids as the temperature decreases, whereas the inverted scenario remains scarce reported. In this work, starting from the coarse-grained ortho-terphenyl model, we build a rigid tetrahedral structure model. It exhibits an earlier decoupling in rotation than in translation. The Stokes-Einstein-Debye relation breaks down while the Stokes-Einstein relation remains intact. The decoupling happens at approximately 2Tg similar as that observed in supercooled water. The rotation shows more heterogeneous dynamics than the translation at all temperatures. Our results suggest that the steric hindrance plays an important role in determining the decoupling between the translational and rotational dynamics.

2026-09-06T13:59:43Z Communications in Theoretical Physics. 2026, 78(9): 95603 Gan Ren 10.1088/1572-9494/ae77c3 http://arxiv.org/abs/2609.05000v1 2026-09-04T11:10:32Z

Sc-alloyed wurtzite nitrides exhibit strongly tunable electromechanical and ferroelectric properties, yet the relationship between their lattice evolution and local bonding environment remains insufficiently established, particularly in Sc$_x$Ga$_{1-x}$N. Here, we investigate the structural and local bonding evolution of Sc$_x$Ga$_{1-x}$N across the dilute-to-intermediate composition range by combining X-ray diffraction, Sc K-edge X-ray absorption near edge structure (XANES), extended X-ray absorption fine structure (EXAFS) and first-principles calculations. Sc incorporation produces an anisotropic lattice expansion and a progressive reduction in the c/a ratio. XANES and EXAFS reveal a concurrent modification of the local environment around Sc, with the effective Sc-N coordination number increasing from 4.1(4) to 4.5(2) and the average Sc-N bond length increasing from 2.045(7) to 2.081(8)Å over x=0.06-0.26. The local response is accompanied by a reduction in the Sc K-edge pre-edge intensity, consistent with a gradual reduction of the local tetrahedral asymmetry. First-principles calculations show that these structural changes are associated with site-selective distortions around Sc and progressive flattening of the structural energy landscape. The calculated intrinsic polarization-switching barrier decreases from 24.2 to 19.0 meV/Å$^3$ with increasing Sc content, while the calculated piezoelectric stress coefficient (e$_{33}$) increases from 0.82 to 1.66~C/m$^2$ and elastic constant (C$_{33}$) decreases from 380 to 227~GPa, resulting in an increase of piezoelectric strain coefficient (d$_{33}$) from 2.99 to 12.46~pC/N. These results show that Sc incorporation progressively modifies the local coordination environment and structural energetics of ScGaN while the long-range wurtzite structure remains preserved over the investigated composition range.

2026-09-04T11:10:32Z 13 pages, 4 figures Shailesh Kalal Gueorgui Kostov Gueorguiev Martin Magnuson Edward Ferraz de Almeida Junior Rohini Sanikop Sagar Jathar Per Sandström Ray-Hua Horng Jens Birch Per Eklund Ching-Lien Hsiao http://arxiv.org/abs/2609.04054v1 2026-09-03T16:31:40Z

We prove a necessary condition conjecture ([27, Conjecture B]) for the maximal singularity of the Hilbert scheme of points in 3D for a large class of degrees, which in particular implies the 1978 Briançon-Iarrobino Conjecture for a tetrahedral degree, and vastly generalises the result in [19]. The novelty lies in introducing a new upper bound on the dimensions of the tangent spaces of the claimed non-maximally singular ideals, constructing canonical ideals that satisfy the claimed maximal singularity condition, providing a lower bound on the dimension of their tangent spaces, and finally comparing the two cases.

2026-09-03T16:31:40Z 18 pages, 12 figures, comments welcome! Fatemeh Rezaee Parsa Saberi http://arxiv.org/abs/2609.02988v1 2026-09-02T15:15:29Z

High-fidelity TCAD simulation of drift-diffusion transport remains the workhorse of emerging FinFET device design, but it is computationally expensive, especially for 3D structures where runtime escalates steeply with mesh complexity. This sharply limits multi-objective design space exploration. Existing machine-learning surrogates map a fixed set of design parameters to a few scalar device metrics, discarding the underlying physics and losing transferability across device geometries and families. A physics-informed graph attention network (GAT) surrogate is proposed. It operates directly on the tetrahedral TCAD mesh and predicts, at every mesh node, the electrostatic potential together with the electron and hole quasi-Fermi levels, the fundamental unknowns of the drift-diffusion system. Training combines a data loss with finite-volume current-continuity residuals, embedding carrier-transport physics into the objective. Operating on the mesh as a graph, the surrogate inherits size generalization: a model trained on few-fin meshes applies unchanged to substantially larger arrays, bounded at inference only by GPU memory. Per-node uncertainty from a deep ensemble drives an active-learning loop that screens large candidate pools in seconds and forwards only the most informative designs for full simulation. Benchmarked against Sentaurus Device on multi-fin tri-gate FinFETs, the surrogate reproduces the three drift-diffusion fields with sub-volt per-field RMSE and reaches a per-design throughput orders of magnitude higher than the full simulator. The advantage grows with device size: on large multi-fin arrays that are prohibitively slow to simulate directly, inference still completes in under a second per device, enabling Pareto-front exploration across device scales infeasible for direct TCAD sweeps.

2026-09-02T15:15:29Z 9 pages, 4 figures, 2 tables. Accepted at IEEE/ACM International Conference on Computer-Aided Design (ICCAD 2026) Leonid Popryho Ayoub Sadeghi Inna Partin-Vaisband 10.1145/3831252.3834249 http://arxiv.org/abs/2609.02666v1 2026-09-02T14:41:53Z

Dipolar liquids combine two coupled degrees of freedom, translational and dipolar. Intriguingly, these two sectors can reside in distinct thermodynamic states, with the state of one sector possibly favoring a specific state of the other. The onset of ferroelectric order in dipolar liquids is an example of this mutual stabilization. Since this coupling is often encoded in interaction potentials, projecting out one sector to derive an effective interaction for the other can uncover the microscopic mechanism underlying this phenomenon. A coarse-grained theory in which the distance between nearest-neighbor particles depends on their dipolar interaction through a density-dependent mechanical compliance shows that a ferroelectric transition can trigger a liquid-liquid transition. It also predicts a first-order liquid-liquid transition in the paraelectric phase that can in turn induce ferroelectric ordering. The anisotropic dipolar-dependent soft-core interaction is shown to lead to an effective Jagla-like isotropic two-length-scale interaction, known to support liquid-liquid phase transitions. Here, however, the two-length-scale pattern depends on density and dipolar configuration, becoming sensitive to dipolar order. Analysis of supercooled TIP4P/Ice water numerical simulations shows that first-coordination-shell features of pair correlation functions are sensitive to dipolar interaction, supporting the coarse-grained theory foundations. Comparison of low- and high-density liquid water reveals enhanced spatial anisotropy of the first coordination shell in the low-density liquid, with increased effective excluded volume, showing that the liquid-liquid transition involves structural changes within the first shell, beyond reorganization of the interstitial region and tetrahedral order. These findings point to a role for dipolar interactions in supercooled water liquid-liquid phase transition.

2026-09-02T14:41:53Z Maria Grazia Izzo http://arxiv.org/abs/2609.02368v2 2026-09-08T01:39:48Z

Ionic transport in oxides is generally frozen at cryogenic temperatures, where thermal energy lies far below typical cation-migration barriers. Neutron powder diffraction reveals progressive Fe/Mg redistribution between tetrahedral (A) and octahedral (B) sites in the spinel Mg0.5Fe0.5TiFeO4 upon cooling from 200 K to 5 K. A-site Fe occupancy increases toward near completion at 5 K within Rietveld resolution, while Ti remains on the B site. This exchange coincides with complex magnetic correlations rather than a classical thermally activated window. Low-temperature magnetostrictive volume changes indicate strong spin-lattice coupling, but do not identify magnetostriction as the sole thermodynamic driver. Room-temperature high-pressure X-ray diffraction produces the opposite occupancy trend, showing that volume contraction alone cannot explain the cryogenic site exchange. These results point to magneto-structural free-energy minimization as a plausible mechanism for unlocking cryogenic cation mobility in a correlated spinel oxide.

2026-09-02T09:40:42Z 17 pages, 4 figures. Submitted to National Science Review. Updated author list; revised manuscript Yifeng Han Yixing Zhao Yunbo Ou Feiran Shen Lunhua He Ligang Xu Mingxue Tang Jared Matteucci Zexiao Zhang Xiaoli Ma Xiaohui Yu Zheng Deng Man-Rong Li Alexandra Navrotsky http://arxiv.org/abs/2608.30863v1 2026-08-31T14:23:16Z

Diffusion processes involving membranes are of fundamental importance in both science and technology, since membranes serve as selective interfaces that regulate the transport of mass, charge, and information across multiple length and time scales. In this study, we employ molecular dynamics (MD) simulations to calculate the self-diffusion coefficient, tetrahedral order parameter and hydrogen-bond (HB) lifetime of SPC/E water over a wide high-temperature range in the presence of thermally activated membranes (TAMs). These membranes exhibit thermally controlled stochastic behavior that locally influences particle dynamics by probabilistically inducing elastic scattering events as particles traverse the membrane. The stochastic behavior of the membranes is governed by a sigmoidal profile, which depend on the reduced temperature of the system. The effective activation energy for diffusion is estimated for several membrane configurations. It is found that the diffusion coefficients generally decrease with an increase in the number of membranes and are in reasonable agreement with the Arrhenius approximation at high temperatures. Additionally, both the tetrahedral order parameter and the HB lifetime are only locally sensitive to the action of the membranes.

2026-08-31T14:23:16Z 11 pages, 7 figures Carlos Handrey A. Ferraz http://arxiv.org/abs/2608.30802v1 2026-08-31T13:54:02Z

Local constraints govern the low-energy physics of frustrated matter, but familiar ice-type rules constrain flux-like quantities and are insensitive to handedness. Here we show that handedness itself can be imposed as an exact local quantum constraint without selecting an axis in spin space. We construct positive-semidefinite, SU(2)-invariant parent Hamiltonians whose complete zero-energy space on a tetrahedron has a prescribed chirality sign, rather than selecting a particular chiral wave function. For spin-1/2 the local term is a rank-one projector onto a chiral tetrahedral singlet, while for arbitrary spin it factorizes as $B^\dagger B$ through a singlet-annihilation operator, with a completely characterized kernel given by the span of the globally rotated chiral color-ice states. For coherent states, the same zero-energy condition becomes an $S$-independent nonlinear constraint in which three spin directions determine the fourth through a Möbius transformation; compositions of these maps define constraint holonomies on extended lattices. Connecting the same local constraint in different ways produces qualitatively different collective regimes: corner-sharing lattices retain exponentially large quantum ground-state kernels, with rigorous lower bounds exceeding conventional ice benchmarks; edge-sharing lattices support subdimensional plane or line zero modes; while triangular constructions suppress nonuniform coherent deformations and contain the complete Anderson tower of tetrahedral magnetic order at exactly zero energy. Two inequivalent triangular coverings further show that harmonic zero-mode counting does not determine the size of the quantum kernel. These results establish a tractable setting in which local handedness, nonlinear constraint geometry, and quantum degeneracy can be disentangled and related directly to the connectivity of the constraint network.

2026-08-31T13:54:02Z 50 pages, 13 figures, 10 tables Péter Kránitz Yasir Iqbal Karlo Penc http://arxiv.org/abs/2609.02932v1 2026-08-28T14:51:02Z

The enumeration of chemical structures traditionally relies on graph- and group-theoretic techniques, including Pólya theory, in order to account for stereochemical symmetries. These methods require bespoke derivations and methods for each molecular family of interest, and quickly become very intricate for nontrivial classes. In this work, we demonstrate that analytic combinatorics provides a unifying, highly extensible, and relatively simple framework for enumeration problems. Using the symbolic method, we show that classical counting problems, such as the enumeration of acyclic alkanes and other hydrocarbon families, can be naturally solved via concise combinatorial specifications of the class of interest. We first demonstrate the simplicity of this approach by replicating existing results in this framework, requiring significantly less work than previously necessary, and then extend these ideas to more complex problems, counting broader classes of molecules accounting for both tetrahedral and E/Z stereoisomerism, counting the distribution of stereogenic units, and enumerating achiral and meso compounds. All results are made reproducible through CombOL, our open-source software package which automates the translation of combinatorial specifications into generating functions using the symbolic method, and performs both univariate and multivariate enumeration.

2026-08-28T14:51:02Z Submitted to J. Math. Chem. 27 pages, 7 figures Casper Asbjørn Eriksen Daniel Merkle http://arxiv.org/abs/2608.28365v1 2026-08-28T14:17:35Z

Understanding how the topology of network forming materials influences their physical properties remains a longstanding challenge. Here, we investigate the topology of experimentally compatible atomistic models of amorphous silica together with the crystalline polymorphs cristobalite and quartz. By comparing multiple atomistic models of amorphous silica that equally reproduce neutron-scattering data, we show that different microscopic descriptions can imply different topological interpretations of glass stability. To characterize the network beyond conventional geometric descriptors, we introduce the linking valence, which quantifies the average number of topological links per network loop. This topological descriptor separates silica into two distinct classes: the mechanically harder quartz exhibit values more than an order of magnitude larger than those of amorphous silica and cristobalite, despite their common tetrahedral building blocks. Spectral analysis of the loop-linking networks provides a complementary distinction, separating amorphous from crystalline phases and revealing differences in the long-range organization of topological constraints. These results establish topological linking as a new framework for connecting the structure and physical properties of network-forming materials.

2026-08-28T14:17:35Z Yair Augusto Gutiérrez Fosado Ayobami Daramola Davide Marenduzzo Ciprian G. Pruteanu http://arxiv.org/abs/2609.29616v1 2026-08-28T09:51:56Z

We prove, to our knowledge, the first unconditional cumulative closure estimates for the Arnold--Mukherjee--Pouly (AMP) refinement algorithm and the original face-marked tetrahedral algorithm of Bänsch on arbitrary conforming initial tetrahedral meshes. Let $T_0,\ldots,T_L$ be an adaptive mesh sequence generated by either algorithm, with $M_\ell\subseteq T_\ell$ denoting the marking set at step $\ell$. Then $$\#T_L-\#T_0\leq C_{\mathrm{clos}}(T_0)\sum_{\ell=0}^{L-1}\#M_\ell.$$ The proof is intrinsic to the physical three-dimensional mesh and requires neither an initial compatibility condition nor a higher-dimensional embedding. It organizes conformity refinements into a causal forest and combines a uniform horizontal-propagation estimate with a weighted packing argument to obtain an explicit closure constant. For the original Bänsch algorithm, every history-dependent resolution of the initial two-edge ambiguity is represented by one of finitely many AMP histories. The estimate therefore holds uniformly for arbitrary deterministic or nondeterministic choices. This resolves a long-standing complexity question for the Bänsch--AMP family.

2026-08-28T09:51:56Z 38 pages Yuwen Li Zhiyuan Yang